Quadrilateral Word Problems
Each example problem that follows uses the steps to solving word problems and the properties of quadrilaterals. Use these problems as a guide to solving quadrilateral word problems.
Example 1
An isosceles trapezoid has base angles of 120°. What is the measure in each of the other angles of the trapezoid?
Read and understand the question. This question is looking for the measure of each of the unknown angles in an isosceles trapezoid. The measures of the base angles are given.
Make a plan. Use the problem solving strategy of drawing a picture to help with this question. In an isosceles trapezoid, the two legs are congruent and the base angles are congruent. The following figure represents this trapezoid.
Carry out the plan. The base angles of the trapezoid are congruent, so each of their measures is 120°. To find the measure of the other angles, subtract the sum of the base angles from 360° and divide by 2: 360 – 240 = 120, = 60° in each of the other angles. Thus, the angles measure 120°, 120°, 60°, and 60°, respectively.
Check your answer. To check this answer, add the measures of the four angles to be sure that the total number of degrees is 360: 120 + 120 + 60 + 60 = 360°, so this answer is checking.
Example 2
A parallelogram has two opposite sides labeled x + 5 units and 2x – 3 units, respectively. What is the length of these opposite sides?
Read and understand the question. This question is looking for the length of each of the opposite sides in a parallelogram.
Make a plan. The lengths of opposite sides of a parallelogram are equal. Set the given expressions equal to each other, and solve for x. Then, substitute the value of x into one of the expressions to find the length of the sides.
Carry out the plan. Set the expressions equal to each other: x + 5 = 2x– 3. Subtract x from each side of the equation to get 5 = x – 3. Add 3 to each side of the equation to get 8 = x. Substitute x = 8 into the expression x + 5. 8 + 5 = 13. The length of each of the opposite sides is 13 units.
Check your answer. To check this answer, substitute x = 8 into the expression 2x – 3 to be sure the value is also 13.
 2(8) – 3 = 16 – 3 = 13
This solution is checking.
Find practice problems and solutions for these concepts at Quadrilateral Word Problems Practice Questions.
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